Air New Zealand, Jetstar and Virgin have several flights per week from Auckland, New Zealand to Rarotonga.
There is also a weekly AirNZ Los Angeles connection and direct Sydney/Rarotonga flight. Book online or see your travel agent for other carriers.

Air Rarotonga has several flights daily to connect you from Rarotonga to Aitutaki and a weekly three island service that includes Atiu.
Note there are no ferries or other ways to get to Aitutaki.